Update WooCommerce billing email after user updates its WP account email

I need to automatically update WooCommerce billing email after any user updates its WP account email. I rebuilt this function for this:

    /* Update woocommerce billing email based on account email */
add_filter( 'profile_update' , 'custom_update_billing_email', 10, 2 );

 function custom_update_billing_email($user_id, $old_user_data ) {
  $current_user = wp_get_current_user();
  
  // Updating Billing info
  
  if($current_user->billing_email != $current_user->user_email)
    update_user_meta($user_id, 'user_email', $current_user->billing_email);
}

Please advise if all is fine since to test the function I’ll need to make actual orders on the site.